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$$S_{\psi^1_{in}, \cdots, \psi^{n_{in}}_{in}, \psi^1_{out}, \cdots, \psi^{n_{out}}_{out}} \;=\; \underset{g \in \mathbb{N}}{\sum} \lambda^g \underset{ {moduli \; space \; of} \atop {{(n_{in},n_{out}) punctured} \atop {{super\; Riemann \; surfaces} \atop {{\Sigma^{n_{in}, n_{out}}_g} \atop {of\; genus\; g}}}} }{ \int } \left( SCFT \; Correlator \; over \; \Sigma \; of \; states\; {\psi^1_{in}, \cdots, \psi^{n_{in}}_{in}, \psi^1_{out}, \cdots, \psi^{n_{out}}_{out}} \right)$$

stringy S-matrix from Polchinski's textbook

stringy S-matrix for the supersymmetric case from Polchinski's textbook